Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:20:01                                   | 
 | -------------------------------------------- | ------------------------------------------------------ | 
 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLA                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 70                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 50; GSD >= .01; EMIN | 
 |                                              | = 0; EMAX = 3                                          | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.04                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.2    64.16280078  1.00000000  .500000000  .000000000  3.00000000
     1.1    49.47063004  1.26067783  3.28247520  .000000000  3.00000000
     2.2    49.03827916  1.32294961  3.21241894  .000000000  3.00000000
     3.1    46.60831197  1.62504998  2.41243124  .000000000  3.00000000
     4.1    45.06939662  1.51072042  2.03666109  .000000000  3.00000000
     5.1    44.38834819  1.33717017  1.81213076  .000000000  3.00000000
     6.1    44.38443539  1.31914785  1.87042316  .000000000  3.00000000
     7.1    44.38171826  1.32373950  1.84561141  .000000000  3.00000000
     8.1    44.38171538  1.32423955  1.84576821  .000000000  3.00000000
     9.1    44.38171528  1.32416274  1.84572826  .000000000  3.00000000

Run stopped after 9 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      163.11828       40.77957
  Residual               66       44.38172         .67245
  Uncorrected Total      70      207.50000

  (Corrected Total)      69       89.20000

  R squared = 1 - Residual SS / Corrected SS =     .50245

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED         1.324162741   .875449440  -.423728461  3.072053944
  GSD        1.845728257  1.358386424  -.866377744  4.557834259
  EMIN        .000000000   .526020030 -1.050232876  1.050232876
  EMAX       3.000000000  1.151275165   .701404969  5.298595031

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000     .6375    -.2147     .8581
  GSD          .6375    1.0000    -.8463     .9132
  EMIN        -.2147    -.8463    1.0000    -.6527
  EMAX         .8581     .9132    -.6527    1.0000

Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:20:01                                   | 
 | -------------------------------------------- | ------------------------------------------------------ | 
 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLB                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 63                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 50; GSD >= .01; EMIN | 
 |                                              | = 0; EMAX = 3                                          | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.04                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.2    67.09468678  1.00000000  .500000000  .000000000  3.00000000
     1.1    63.90171049  1.26438083  3.02368105  .000000000  3.00000000
     2.2    57.21069095  1.55345204  2.70522721  .000000000  3.00000000
     3.1    50.39546580  1.84663020  2.11559792  .000000000  3.00000000
     4.1    47.42089268  2.00335557  1.41919117  .000000000  3.00000000
     5.1    45.90851715  1.87300080  1.16438677  .000000000  3.00000000
     6.1    45.00007175  1.67717532  .910907532  .000000000  3.00000000
     7.1    44.99128867  1.68254411  .859895773  .000000000  3.00000000
     8.1    44.99050889  1.67786227  .862227626  .000000000  3.00000000
     9.1    44.99050309  1.67832732  .862826972  .000000000  3.00000000
    10.1    44.99050308  1.67833978  .862888938  .000000000  3.00000000

Run stopped after 10 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4       93.75950       23.43987
  Residual               59       44.99050         .76255
  Uncorrected Total      63      138.75000

  (Corrected Total)      62       91.60317

  R squared = 1 - Residual SS / Corrected SS =     .50885

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED         1.678339780   .355884282   .966216977  2.390462584
  GSD         .862888938   .415249467   .031976674  1.693801203
  EMIN        .000000000   .182822488  -.365826954   .365826954
  EMAX       3.000000000   .691927470  1.615456331  4.384543669

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000     .6570     .0233     .8732
  GSD          .6570    1.0000    -.4504     .8136
  EMIN         .0233    -.4504    1.0000    -.2491
  EMAX         .8732     .8136    -.2491    1.0000

Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:20:01                                   | 
 | -------------------------------------------- | ------------------------------------------------------ | 
 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLC                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 54                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 50; GSD >= .01; EMIN | 
 |                                              | = 0; EMAX = 3                                          | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.04                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.2    31.52677442  1.00000000  .500000000  .000000000  3.00000000
     1.3    27.97637476  .843615511  1.17229657  .000000000  3.00000000
     2.1    27.97509696  .836983999  1.16841329  .000000000  3.00000000
     3.1    27.97427713  .838301655  1.16109798  .000000000  3.00000000
     4.1    27.97403356  .839600098  1.15440731  .000000000  3.00000000
     5.1    27.97403355  .839601839  1.15445159  .000000000  3.00000000

Run stopped after 5 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4       97.77597       24.44399
  Residual               50       27.97403         .55948
  Uncorrected Total      54      125.75000

  (Corrected Total)      53       62.37500

  R squared = 1 - Residual SS / Corrected SS =     .55152

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED          .839601839   .700146496  -.566683785  2.245887463
  GSD        1.154451586   .755941794  -.363902193  2.672805365
  EMIN        .000000000   .285790138  -.574026386   .574026386
  EMAX       3.000000000  1.289209330   .410546853  5.589453147

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000     .8109    -.3025     .9509
  GSD          .8109    1.0000    -.7095     .9108
  EMIN        -.3025    -.7095    1.0000    -.5193
  EMAX         .9509     .9108    -.5193    1.0000

